# Confidence in temperature

• May 25th 2011, 04:18 AM
JMan69
Confidence in temperature
Using column temp, we can compute the sample mean
temp = 19:74, sample size = 150 and the sample standard deviation stemp = 6:035.
(a) Construct a 91% confidence interval for the population mean of

temp.
(b) If we want ensure the error margin of the 91% confidence interval to be less than 0.5, what sample size should we take (assuming that the sample standard deviation is a good estimate of the population standard deviation)?
is the error margin of the 91% confidence interval different to the error margin of x-bar? (s\sqrt{n}), how would you calc the approx sample size?
2. Construct a 95% confidence interval for the proportion of forest fires that occur when the temperature is greater than 25 degrees celsius.
I found the values in the data set >25 degrees which made n=21, x-bar=28.533 and s=2.467, then I just did the normal confidence interval formula to work it out. Did I go about that the right way?;)

Cheers,

Jay
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• May 26th 2011, 09:41 PM
matheagle
well, there is a slight distinction.....
IF the data is normal then this is a t with 149 df, which is darn close to a N(0,1)
IF the data is not from a normal distribution then you can use the CLT and get an approximate CI using the Z.

$\bar X \pm t_{n-1,\alpha/2}S/\sqrt{n}$

or $\bar X \pm Z_{\alpha/2}S/\sqrt{n}$

Next use $Z_{\alpha/2}S/\sqrt{n}\le .5$ and solve for the smallest n that works.